Fly to one of Switzerland’s international airports Zurich or Geneva (which ever airport is best for you) and from there take the train to Biel. It takes around 1 1/2 hours from both airports to get to Biel by train. There is a direct train from both airports.
Several European cities fly to the airport Bern Belp. This small airport makes traveling much easier and more enjoyable. From here you will get to Biel by bus and train.
For more informations about train/bus tickets and timetable please click here. If you are planning to extend your stay in Switzerland a Swiss Travel Pass could be interesting for you. If you are only taking the train from the airport to Biel and back, a Swiss Transfer Ticket will be best for you.